Having illnesses and/or disabilities is bad enough by itself, but these may also impact the cost of car insurance, as well as raise the possibility of your not being able to get insured at all. However, by and large the system is operated fairly; and a realistic assessment is usually made about your ability to drive safely, which is in the best interests of not only yourself but other road users as well.
It is a legal requirement to inform the DVLA of any medical, physical or mental issues that you may have, which could decrease your ability to drive safely. Once you have informed the DVLA they will ask you a number of questions, and then a decision will be made upon whether or not you will be allowed to continue driving. Under normal circumstances you would be allowed to continue driving as normal until a decision had been reached, which is usually made within about six weeks. You can get more information about the issues you must tell them about at this government website.
They may write to your general practitioner or consultant, and may require you to be examined by an independent doctor.
In the meanwhile it would be essential that you contacted your insurer to inform them of the situation. They will want to know more about your condition, and if they feel that it is sufficiently serious as to warrant an increase in premium they can charge you this, but they must give you their reasons for doing so. You are within your rights to challenge this if you disagree with their verdict.
Failing to inform them could well invalidate your insurance cover completely.
If you become disabled, either permanently or temporarily, it may be necessary to drive a car which has been adapted specially for your needs. This would probably mean that it would be more expensive to repair in the event of an accident, and therefore your insurers would probably increase your premium to cover this extra risk.
Unfortunately medical conditions can complicate driving licence and insurance issues considerably, and you may well find that the help of a specialist broker can be invaluable.